In addition to these models, there exists a more recent DFTB energy expression, where third-order density fluctuation terms are included in the Kohn-Sham energy expansion[1]}, [2]}. This yields an additional charge-transfer term to Equation REF , namely,
\(E^3_\mathrm {Coul} = \frac{1}{6} \int \int ^{^{\prime }} \int ^{^{\prime \prime }} \left(\frac{\delta ^3 E_{xc}[n_0]}{\delta n\, \delta n^{^{\prime }} \delta n^{^{\prime \prime }}}\right) \times \delta n\, \delta n^{^{\prime }} \delta n^{^{\prime \prime }}.\) 
